0,1

In the Frey-Sellers reference this sequence is called {(n+2) over 3}_{2}, n >= 0.

If X is an n-set and Y a fixed (n-3)-subset of X then a(n-3) is equal to the number of 3-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007

D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

Milan Janjic, Two Enumerative Functions

a(n)= A062745(n+2, 3)= binomial(n+4, 3)-1 = (n+1)*(n^2+8*n+18)/3!.

G.f.: N(3;1, x)/(1-x)^4 with N(3;1, x)=3-3*x+x^2, polynomial of the second row of A062746.

a(n)=((n^3-n)/6)-1,n>=3 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 05 2007

a(n)=A000292(n+2)-1 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 05 2007

a(n)=A000292(n+1)-1. a(n)=sum of n successive triangular numbers A000217 starting from n=2 a(n)=Sum[n(n+1)/2,{n,2,n}]=Sum[C(n+1,2),{n,2,n}] - Artur Jasinski (grafix(AT)csl.pl), Mar 14 2008

[seq(binomial(n, 3)-1, n=4..41)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006

a:=n->sum ((j+1)*j/2, j=2..n): seq(a(n), n=2..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2006

seq(((n^3-n)/6)-1, n=3..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 05 2007

seq(sum(sum(sum(1, k=0..l), l=0..m), m=1..n), n=1..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 26 2008

k = 0; a = {}; Do[f = n(n + 1)/2; k = k + f; AppendTo[a, k], {n, 2, 100}]; a - Artur Jasinski (grafix(AT)csl.pl), Mar 14 2008

A column of triangle A014473.

Sequence in context: A146184 A155274 A058058 this_sequence A147174 A147158 A014540

Adjacent sequences: A062745 A062746 A062747 this_sequence A062749 A062750 A062751

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001

More terms from Artur Jasinski (grafix(AT)csl.pl), Mar 14 2008